TABLE OF CONTENTS We consider univariate polynomials
cf. (1.3) and Definition 1.4. Only when we explicitly say so, we assume p( x; a) to be monic, i.e. to have ? n = 1. In the data space 
, our standard norm ..* is a weighted maximum norm; cf. section 3.1.1.
Intrinsic univariate polynomials (whose coefficients are assumed as exact; cf. Definition 3.1) have been an object of mathematical investigation for centuries; their analytic and algebraic properties are well known, and even their numerical analysis is rather complete. We only recall some basic facts about such polynomials in the following section; then we devote our attention to aspects which come to light when some or all of the coefficients are empirical.
From the analytic point of view, univariate polynomials with real or complex coefficients are uniformly analytic or holomorphic functions from 
, where-as agreed in section 1.2- 
denotes the affine complex plane, i.e. 
: They are holomorphic in each point of 
; cf. Proposition 1.4. For 
is the zero polynomial, and the Taylor expansion of p at any 
is finite and at most of length n. Even if p( x; a) has real coefficients, it is often helpful to regard it as a function from 
Since 
, there are at most n ? 1 points ? ?
